The first two parts are not really physics questions, I am leaving the question because there is physics in part (3). The plate hides the motor and does not significantly effect the air flow because the the blades don't more much air there. The cage protects your fingers at least as much as the blades.
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dmckee♦Apr 23 '11 at 14:42

As for the cage, it seems to me protecting the fingers is more important than protecting the blades. Just sayin'.
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hyperpolarizerSep 28 '13 at 7:13

3 Answers
3

To the last comment - I disagree. Wind turbines operate in a fairly different flow regime, and compare the table fan to the prop of a ship, they are about the same shape. The key difference is moving fluid volume. The larger blades push against the fluid more strongly, which is desirable in the fan case and in the ship case. Wind turbines are different as the builder cares nothing about the exhaust wind.

Anyway...
1. I don't think it's 'functional' in any sense other than the fact that the motor is behind it.
2. I don't believe so and I agree with other commentators that the fan would be more simple and less noisy without them. I'll withhold comment on the obvious safety considerations.
3. Everything dealing with pumping or pushing a fluid makes noise, and it is quite considerable. You could remove the blades and listen to the electric motor itself and you would find it constitutes only a small fraction of the noise. Noise minimization for fans is a major engineering topic and it's more or less impossible to reduce it. Obviously, the faster you get the bigger of a problem it is. I believe we're talking about turbulent flow in general, I don't think many pumps are actually laminar. The metal bars will have an influence, but I could not say how much.

I won't address the details of the fluid dynamics that cause the cage to produce noise because it is well out of my area of expertise. But I have performed an experiment in my office. The small desk fan I bought was too noisy. Since it lives on the top of a tall bookcase and well out of reach, I removed the cage completely. It is a lot quieter now.

My guess is that turbulence around the bars of the cage causes the noise. With the cage removed, the air stream throws further. There is still some noise, so I'm guessing that the fan's blades are not optimally shaped.

I suspect the cage does generate turbulence on a small spatial scale. I remember riding by bike across an overpass, an experiencing severe wind pressure, sideways when going through a portion enclosed in a wire fence, so I suspect this low level turbulence has some effect on macroscopic parameters such as drag. I doubt the cage it designed as a turbulence generator, rather it is mandated to keep fingers out.
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Omega CentauriApr 24 '11 at 4:13

I'm sure that there was no design goal other than keeping small fingers out of the blades. I demonstrated the overall safety of the cover-less fan by stopping it without damage (or any real pain, even) with my own fingers. It also moves more air than it did with the cage in place. Cheap fans are cheap.
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RBerteigJan 17 '14 at 2:22

A related question. Compare a table fan's blades versus a wind turbines blades. It is obvious that the former covers more than half the area of the disk prescribed by its circumference, but the wind turbines swept area is mostly empty air. I've heard the power of a wind turbine depends upon the swept area, which implies that the blades already cover enough area, so I would surmise the table fan is probably seriously inoptimal. Probablt the blades are as wide as they are because of pschological marketting, rather than aerodynamics. Does anyone know if this is in fact the case?

Since table fan blades have been that shape since table fans have existed, my personal guess is that they've essentially never been modeled or designed. They just work well enough, and they look "right" enough. A lot of wind turbines actually look like they shouldn't work at all as a result.
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RBerteigApr 24 '11 at 19:42

I use window (box) fans to bring cold air in on summer nights. At 90watts a piece I wish I could get something more energy efficient. Googling for high efficiency fans doesn't do the trick (unless you want a 36inch barn ventillation fan).
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Omega CentauriApr 24 '11 at 20:48